What are the zeros of the quadratic function f(x) = 2x2 + 8x – 3? x = –2 – and x = –2 + x = –2 – and x = –2 + x = 2 – and x = 2 + x = 2 – and x = 2 +

The given quadratic function is:

[tex]f(x)=2 x^{2} +8x-3[/tex]

The zeros of the quadratic functions also known as its roots can be found using the quadratic formula.

According to the quadratic formula:

[tex]x= \frac{-b+- \sqrt{ b^{2}-4ac } }{2a} [/tex]
here,
b = coefficient of x-term
a = coefficient of x²-term
c = costant term

For given function:
a = 2
b = 8
c = - 3

Using these values in the formula, we get:

[tex]x= \frac{-8+- \sqrt{64-4(2)(-3)} }{2(2)} \\ \\ x= \frac{-8+- \sqrt{88} }{4} \\ \\ x= \frac{-8+-2 \sqrt{22}}{4} \\ \\ x= \frac{-4+- \sqrt{22} }{2} \\ \\ x= \frac{-4+ \sqrt{22} }{2}, x= \frac{-4- \sqrt{22} }{2} [/tex]

Thus, these values of x are the zeros of the given quadratic function f(x)=2x²+8x-3